Results: cars2.sas

Regression on Metric Cars Data

Look at input data set

The Print Procedure

Data Set WORK.CARS

Obs Cntry lper100k weight length
1 US 19.8 2178 5.92
2 Japan 9.9 1026 4.32
3 US 10.8 1188 4.27
4 US 12.5 1444 5.11
5 US 12.5 1485 5.03
6 US 12.5 1485 5.03
7 Europ 10.4 972 4.37
8 US 13.2 1665 5.44
9 Europ 17 1539 4.88
10 US 9.2 1003 4.32
11 Japan 7.9 891 3.91
12 US 11.9 1273 4.95
13 US 11.3 1930 5.18
14 Europ 9.2 823 3.61
15 Japan 13.2 1084 4.42
16 US 8.2 949 4.14
17 US 19.8 2178 5.92
18 US 17 1755 5.18
19 Europ 14 1426 4.9
20 Japan 7.7 990 4.19
21 US 17 1827 5.61
22 US 9.2 1134 4.62
23 US 14.9 1813 5.23
24 Europ 9.5 1192 4.5
25 Japan 11.3 1237 4.67
26 US 17 1858 5.51
27 US 14.9 1813 5.23
28 US 8.5 1062 4.32
29 US 10.8 1431 4.9
30 US 13.2 1651 5.54
31 Japan 13.2 1201 4.45
32 US 8.5 1062 4.32
33 Japan 9.5 1008 4.37
34 US 17 1858 5.51
35 US 10.8 1318 4.72
36 US 12.5 1440 5.05
37 Europ 14 1273 4.8
38 Europ 5.8 918 3.94
39 US 14.9 1813 5.23
40 US 12.5 1530 5.08
41 US 14 1683 5.59
42 US 15.9 1836 5.64
43 US 17 1723 5.11
44 US 11.3 1827 5.59
45 US 10.8 1449 5.08
46 US 10.8 1318 4.72
47 US 17 1858 5.51
48 US 11.9 1273 4.95
49 Europ 9.5 868 3.94
50 US 10.8 1318 4.72
51 US 13.2 1665 5.44
52 US 13.2 1620 5.23
53 US 7.9 954 4.14
54 US 7.9 954 4.14
55 US 12.5 1516 5.08
56 US 13.2 1665 5.44
57 US 11.9 1462 4.98
58 Europ 10.4 972 4.37
59 US 13.2 1665 5.44
60 US 15.9 1674 5.38
61 US 17 1755 5.18
62 Japan 13.2 1201 4.45
63 US 9.9 1237 4.55
64 US 19.8 2178 5.92
65 US 11.3 1930 5.18
66 US 8.5 1062 4.32
67 Japan 6.8 922 4.17
68 Japan 9.9 1026 4.32
69 US 10.8 1449 5.08
70 US 9.2 1134 4.62
71 US 9.5 990 4.19
72 Japan 13.2 1084 4.42
73 US 11.3 1930 5.18
74 US 13.2 1516 5.03
75 US 14 1507 4.39
76 Japan 13.2 1084 4.42
77 Japan 9.9 1026 4.32
78 Europ 11.3 958 4.09
79 US 17 1858 5.51
80 US 11.3 1930 5.18
81 US 11.3 1192 4.55
82 US 9.9 1237 4.55
83 Europ 5.8 918 3.94
84 US 14.9 1813 5.23
85 US 10.8 1449 5.08
86 US 17 1755 5.18
87 US 13.2 1561 5.03
88 US 8.5 1062 4.32
89 US 12.5 1489 5.03
90 US 11.3 1192 4.55
91 US 17 1827 5.61
92 US 17 1755 5.18
93 US 14 1683 5.59
94 US 19.8 2178 5.92
95 Europ 5.8 918 3.94
96 Europ 5.8 918 3.94
97 Europ 14 1426 4.9
98 US 9.5 990 4.19
99 US 14.9 1660 5.38
100 US 13.2 1498 5.11

Regression on Metric Cars Data

Check dummy variables

The FREQ Procedure

The Freq Procedure

Table c1 * Country

Cross-Tabular Freq Table

Frequency
Table of c1 by Country
c1(US = 1) Country(Location of Head Office)
Europ Japan US Total
0
14
13
0
27
1
0
0
73
73
Total
14
13
73
100

Table c2 * Country

Cross-Tabular Freq Table

Frequency
Table of c2 by Country
c2(Europe = 1) Country(Location of Head Office)
Europ Japan US Total
0
0
13
73
86
1
14
0
0
14
Total
14
13
73
100

Regression on Metric Cars Data

Litres per 100 k Broken Down by Country

The MEANS Procedure

The Means Procedure

Summary statistics

Analysis Variable : lper100k Litres per 100 kilometers
Location of Head Office N Obs N Mean Std Dev Minimum Maximum
Europ 14 14 10.1785714 3.6190051 5.8000000 17.0000000
Japan 13 13 10.6846154 2.3632062 6.8000000 13.2000000
US 73 73 12.9643836 3.1325518 7.9000000 19.8000000

Regression on Metric Cars Data

Regression with Just Country

The REG Procedure

Model: MODEL1

Dependent Variable: lper100k Litres per 100 kilometers

The Reg Procedure

MODEL1

Fit

lper100k

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 129.10371 64.55185 6.63 0.0020
Error 97 943.80789 9.72998    
Corrected Total 99 1072.91160      

Fit Statistics

Root MSE 3.11929 R-Square 0.1203
Dependent Mean 12.27800 Adj R-Sq 0.1022
Coeff Var 25.40553    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 10.68462 0.86514 12.35 <.0001
c1 US = 1 1 2.27977 0.93901 2.43 0.0170
c2 Europe = 1 1 -0.50604 1.20144 -0.42 0.6745

Regression on Metric Cars Data

Regression with Just Country

The REG Procedure

Model: MODEL1

Test USvsEURO

Results

Test USvsEURO Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 1 91.16650 9.37 0.0029
Denominator 97 9.72998    

Regression on Metric Cars Data

Compare Oneway with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Country 3 Europ Japan US

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Regression on Metric Cars Data

Compare Oneway with proc glm

The GLM Procedure

 

Dependent Variable: lper100k Litres per 100 kilometers

Analysis of Variance

lper100k

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 129.103708 64.551854 6.63 0.0020
Error 97 943.807892 9.729978    
Corrected Total 99 1072.911600      

Fit Statistics

R-Square Coeff Var Root MSE lper100k Mean
0.120330 25.40553 3.119291 12.27800

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
Country 2 129.1037082 64.5518541 6.63 0.0020

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Country 2 129.1037082 64.5518541 6.63 0.0020

Box Plot

Fit Plot for Litres per 100 kilometers by Location of Head Office

Regression on Metric Cars Data

Country, Weight and Length

The REG Procedure

Model: MODEL1

Dependent Variable: lper100k Litres per 100 kilometers

The Reg Procedure

MODEL1

Fit

lper100k

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 797.30574 199.32644 68.71 <.0001
Error 95 275.60586 2.90111    
Corrected Total 99 1072.91160      

Fit Statistics

Root MSE 1.70327 R-Square 0.7431
Dependent Mean 12.27800 Adj R-Sq 0.7323
Coeff Var 13.87250    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -5.28270 2.92605 -1.81 0.0742
c1 US = 1 1 -1.99424 0.58499 -3.41 0.0010
c2 Europe = 1 1 -0.50652 0.66016 -0.77 0.4448
weight Weight in kg 1 0.00546 0.00147 3.71 0.0004
length Length in meters 1 2.34597 0.98033 2.39 0.0187

Regression on Metric Cars Data

Country, Weight and Length

The REG Procedure

Model: MODEL1

Test country

Results

Test country Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 2 20.01754 6.90 0.0016
Denominator 95 2.90111    

Regression on Metric Cars Data

Country, Weight and Length

The REG Procedure

Model: MODEL1

Test USvsEURO

Results

Test USvsEURO Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 1 19.37833 6.68 0.0113
Denominator 95 2.90111    

Regression on Metric Cars Data

Country, Weight and Length

The REG Procedure

Model: MODEL1

Test wgt_len

Results

Test wgt_len Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 2 334.10102 115.16 <.0001
Denominator 95 2.90111    

Regression on Metric Cars Data

Proportion of remaining variation

The IML Procedure

_LIT1001

Country controlling for Weight and Length

a

a
0.1268382

_LIT1006

Weight and Length controlling for Country

a

a
0.7079798

Regression on Metric Cars Data

Country, weight and length with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
Country 3 Europ Japan US

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Regression on Metric Cars Data

Country, weight and length with proc glm

The GLM Procedure

 

Dependent Variable: lper100k Litres per 100 kilometers

Analysis of Variance

lper100k

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 4 797.305741 199.326435 68.71 <.0001
Error 95 275.605859 2.901114    
Corrected Total 99 1072.911600      

Fit Statistics

R-Square Coeff Var Root MSE lper100k Mean
0.743123 13.87250 1.703266 12.27800

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
weight 1 746.6769100 746.6769100 257.38 <.0001
length 1 10.5937459 10.5937459 3.65 0.0590
Country 2 40.0350853 20.0175427 6.90 0.0016

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
weight 1 39.86971491 39.86971491 13.74 0.0004
length 1 16.61365020 16.61365020 5.73 0.0187
Country 2 40.03508534 20.01754267 6.90 0.0016

Regression on Metric Cars Data

Country, weight and length with proc glm

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Bonferroni

Least Squares Means

Country

lper100k

LSMeans

Country lper100k LSMEAN LSMEAN Number
Europ 13.2981897 1
Japan 13.8047068 2
US 11.8104679 3

Difference Matrix

Least Squares Means for Effect Country
t for H0: LSMean(i)=LSMean(j) / Pr > |t|

Dependent Variable: lper100k
i/j 1 2 3
1
 
 
-0.76727
1.0000
2.584495
0.0338
2
0.767266
1.0000
 
 
3.408986
0.0029
3
-2.5845
0.0338
-3.40899
0.0029
 
 

Regression on Metric Cars Data

Country, Weight and Length with Interactions

The REG Procedure

Model: MODEL1

Dependent Variable: lper100k Litres per 100 kilometers

The Reg Procedure

MODEL1

Fit

lper100k

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 8 817.63884 102.20486 36.43 <.0001
Error 91 255.27276 2.80520    
Corrected Total 99 1072.91160      

Fit Statistics

Root MSE 1.67487 R-Square 0.7621
Dependent Mean 12.27800 Adj R-Sq 0.7412
Coeff Var 13.64124    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 -10.07335 16.83584 -0.60 0.5511
c1 US = 1 1 5.01091 17.14931 0.29 0.7708
c2 Europe = 1 1 -1.83239 18.58103 -0.10 0.9217
weight Weight in kg 1 0.01692 0.01024 1.65 0.1019
length Length in meters 1 0.64989 5.94151 0.11 0.9131
cw1   1 -0.01123 0.01036 -1.08 0.2810
cw2   1 -0.01035 0.01171 -0.88 0.3793
cL1   1 1.18552 6.03345 0.20 0.8447
cL2   1 2.83971 6.70494 0.42 0.6729

Regression on Metric Cars Data

Country, Weight and Length with Interactions

The REG Procedure

Model: MODEL1

Test country

Results

Test country Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 2 0.98337 0.35 0.7052
Denominator 91 2.80520    

Regression on Metric Cars Data

Country, Weight and Length with Interactions

The REG Procedure

Model: MODEL1

Test Interactions

Results

Test Interactions Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 4 5.08328 1.81 0.1333
Denominator 91 2.80520    

Regression on Metric Cars Data

Weight and length are now centered: Mean=0

The REG Procedure

The Reg Procedure

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Descriptive Statistics

Descriptive Statistics
Variable Sum Mean Uncorrected SS Variance Standard
Deviation		 Label
Intercept 100.00000 1.00000 100.00000 0 0 Intercept
c1 73.00000 0.73000 73.00000 0.19909 0.44620 US = 1
c2 14.00000 0.14000 14.00000 0.12162 0.34874 Europe = 1
weight -3.638E-12 -3.638E-14 12969899 131009 361.95176 Weight in kg (Centered)
length 3.10862E-14 3.10862E-16 29.93794 0.30240 0.54991 Length in cm (Centered)
cw1 9255.67000 92.55670 8908732 81334 285.19102  
cw2 -4663.94000 -46.63940 2307825 21114 145.30712  
cL1 14.37840 0.14378 19.35176 0.17459 0.41784  
cL2 -7.76880 -0.07769 6.83496 0.06294 0.25089  
lper100k 1227.80000 12.27800 16148 10.83749 3.29203 Litres per 100 kilometers

Regression on Metric Cars Data

Weight and length are now centered: Mean=0

The REG Procedure

Model: MODEL1

Dependent Variable: lper100k Litres per 100 kilometers

MODEL1

Fit

lper100k

Number of Observations

Number of Observations Read 100
Number of Observations Used 100

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 8 817.63884 102.20486 36.43 <.0001
Error 91 255.27276 2.80520    
Corrected Total 99 1072.91160      

Fit Statistics

Root MSE 1.67487 R-Square 0.7621
Dependent Mean 12.27800 Adj R-Sq 0.7412
Coeff Var 13.64124    

Parameter Estimates

Parameter Estimates
Variable Label DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept Intercept 1 16.99193 1.70891 9.94 <.0001
c1 US = 1 1 -5.11069 1.72204 -2.97 0.0038
c2 Europe = 1 1 -2.68732 1.88066 -1.43 0.1564
weight Weight in kg (Centered) 1 0.01692 0.01024 1.65 0.1019
length Length in cm (Centered) 1 0.64989 5.94151 0.11 0.9131
cw1   1 -0.01123 0.01036 -1.08 0.2810
cw2   1 -0.01035 0.01171 -0.88 0.3793
cL1   1 1.18552 6.03345 0.20 0.8447
cL2   1 2.83971 6.70494 0.42 0.6729

Regression on Metric Cars Data

Weight and length are now centered: Mean=0

The REG Procedure

Model: MODEL1

Test country

Results

Test country Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 2 24.03294 8.57 0.0004
Denominator 91 2.80520    

Regression on Metric Cars Data

Weight and length are now centered: Mean=0

The REG Procedure

Model: MODEL1

Test Interactions

Results

Test Interactions Results for Dependent Variable lper100k
Source DF Mean
Square		 F Value Pr > F
Numerator 4 5.08328 1.81 0.1333
Denominator 91 2.80520